An old law-school building in the University District could become the next hub of startup innovation in Seattle.

TechStars and Founders Co-op are leaving their space at 511 Boren Ave. in South Lake Union and moving into Condon Hall next year. The space, which used to house the University of Washington Law School, is about four blocks from the UW campus

Chris DeVore, who runs both organizations, said that he sees the U District as the up-and-coming neighborhood for startups as they’re priced out of South Lake Union.

Startups need inexpensive office space, DeVore said, and the combination of the new Amazon towers and other bigoffice buildings in South Lake Union are really pushing the startups out. “It really sucks the air out of the room for the startups,” he said.

It’s only a matter of time, DeVore said, before a big tech company that wants to be close to tech talent moves into the U District. “There are a number of big (tech) firms that are not in any neighborhood of any kind and want to be,” DeVore said.

The city is also working on updating the U District’s zoning to allow taller buildings, something that’s likely to attract those large tenants.

This is the direction things are moving, DeVore said, and his organizations are just a footnote in a larger story that's just getting started in the neighborhood. "We're going to really make something exciting here," he said.